Question: Mandy works construction. She knows that a $5$ meter long metal bar has a mass of $40 \text{ kg}$. Mandy wants to figure out the mass $(w)$ of a bar made out of the same metal that is $3$ meters long and the same thickness. What is the mass of the shorter bar?
Solution: We're dealing with a proportional relationship, so each ratio of kilograms to meters must be equivalent. Let's use a table to see the mass of a one-meter-long metal bar. ${8}$ $\longrightarrow$ ${1}$ ${40}$ $\longrightarrow$ ${5}$ $ \times {\dfrac{1}{5}}$ $ \times {\dfrac{1}{5}}$ ${{kg}}$ $\longrightarrow$ ${{m}}$ The mass of a one-meter-long metal bar is ${8} \text{ kg}$. Now, we can use this rate to solve for the mass of a $3$ meter long metal bar. $w$ $\longrightarrow$ ${3}$ ${{8}}$ $\longrightarrow$ ${1}$ $ \times {3}$ $ \times {3}$ ${40}$ $\longrightarrow$ ${5}$ ${{kg}}$ $\longrightarrow$ ${{m}}$ $w={8}\times3=24$ The mass of the shorter bar is $24 \text{ kg}$.